Two issues regarding suppression calculation:
1) overhead.cpp CalcSuppressionTolerance()

bTolerance += pSoldier->GetSuppressionResistanceBonus();

is calculated after applying minimum and maximum suppresion tolerance values

bTolerance = __max(bTolerance, gGameExternalOptions.ubSuppressionToleranceMin);
bTolerance = __min(bTolerance, gGameExternalOptions.ubSuppressionToleranceMax);

This could lead to incorrect suppression tolerance values.
Changed this to

// Flugente: add personal bonus to suppresion tolerance
bTolerance += pSoldier->GetSuppressionResistanceBonus();

bTolerance = __max(bTolerance, gGameExternalOptions.ubSuppressionToleranceMin);
bTolerance = __min(bTolerance, gGameExternalOptions.ubSuppressionToleranceMax);

overhead.cpp patch r6663

2) values in backgrounds.xml are probably too excessive. Adding or deducting 10 or 20 from suppression tolerance (min 1, max 18) makes all other calculations rather meaningless.
So i suggest reducing this to appropriate values, as backgrounds are supposed to make very small changes to other systems.
I changed them to 1/5 of original values, so now Barry has -2 penalty to suppression tolerance instead of -10, because of his graduate background.
backgrounds.xml patch gamedir 1885
This change is subject to discussion. Maybe original values were supposed to be % penalties?